149 Draw the line
(PW) set the limit
He sets an early curfew for his children. He draws the line at 10:00PM.
(free)
1. To decide firmly an arbitrary boundary between two things: "Where do you draw the line between your own decisions and those of your superiors?" (Robert Marion).
2. To decide firmly the limit of what one will tolerate or participate in: The officer committed fraud but drew the line at blackmail.
(your)or draw a line
to set a limit
(usingEnglish)
When you draw the line, you set out limits of what you find acceptable, beyond which you will not go.
(phraseFinder)
I think "cross the line" does have a negative connotation. As in, going beyond the boundaries of good taste. Regarding the other question, it is hard to tell which phrase came first -- draw the line or draw the line in the sand. From the archives:
DRAW THE LINE - "When we say 'This is where I draw the line,' we are of course laying down a definite limit beyond which we refuse to go. Several attempts have been made to trace actual sources of the figurative 'line' in the phrase. One says that it referred to tennis, a sport almost as popular as cricket in England by the 18th century. When tennis was introduced from France four centuries before, according to this story, there were no exact dimensions for the court and players drew lines beyond which they agreed the ball couldn't be hit. Another explanation says that the line was cut by a plowhorse across a field to indicate the boundary of a farmer's holding in 16th-century England. No examples of the figurative expression 'to draw the line' have been found recorded before 1793, but either theory could be right. The phrase could also derive from early prizefights, where a line was drawn in the ring that neither fighter could cross." From "Encyclopedia of Word and Phrase Origins" by Robert Hendrickson (Facts on File, New York, 1997).
DRAW A LINE IN THE SAND -- ". The most recent use of the phrase 'draw a line in the sand' was, of course, by President George Bush at the beginning of the Gulf War. But for the true clue as to the origin of the phrase, we turn to my esteemed colleague William Safire, whom I especially esteem when he does my work for me. In his book 'In Love With Norma Loquendi' (a collection of his Sunday New York Times Magazine columns, published by Random House in 1994), Mr. Safire provides two possible origins for 'drawing a line in the sand.'
The more recent possible origin for the phrase is an incident said to have taken place during the siege of the Alamo in 1836, when William Barret Travis drew a line in the sand with his sword and urged those willing to stay and defend the fort to step across it. Unfortunately, this heroic story seems to have been invented by a 19th century promoter long after the fall of the Alamo. But the myth itself probably greatly popularized the phrase, so it does count as an origin of sorts even if the incident itself was apocryphal.
Another possible origin dates back to the time of the Roman Empire. It seems that one of the Macedonian kings, a bit short of cash, decided to invade Egypt, then a Roman protectorate. His army was met at the border by a lone Roman senator named Popillius Laenas, who ordered the king to withdraw. The king began to stall for time, so Popillius Laenas drew a circle in the sand around the king and demanded that the king agree to withdraw his army before he stepped out of the circle. The king, apparently impressed by the senator's nerve (or, more likely, by the Roman Empire in general), withdrew. Incidentally, not only is this account verified by contemporary historians, but it also may be the only known instance of a line drawn in the sand actually stopping someone."
http://www.word-detective.com/back-e2.html#lineinsand
